Pips answers for Tuesday, June 30, 2026

Start with the 4 region at the top: only 0 + 0 + 0 + 4, or 0 + 0 + 2 + 2 can make it with these dominoes.

• the 4 region at the top: 0, 0, 2, 2
• the single-cell 4 region at the left: 4
• the “=” region at the center: 5, 5
• the single-cell “<2” region at the right: 0
• the single-cell “<5” region at the bottom: 1

1. The single-cell 4 region at the left needs a total of exactly 4 — 2 placements fit here for now, but every other one leaves some region impossible a few moves later. Place the 0–4 domino vertically on row 1, column 1 and row 2, column 1.
2. The 4 region at the top needs a total of exactly 4 (1 of its 4 cells is already filled) — 3 placements fit here for now, but every other one leaves some region impossible a few moves later. Place the 0–0 domino vertically on row 1, column 4 and row 2, column 4.
3. The 4 region at the top needs a total of exactly 4 (2 of its 4 cells are already filled) — 3 placements fit here for now, but every other one leaves some region impossible a few moves later. Place the 2–2 domino horizontally on row 1, column 2 and row 1, column 3.
4. The “=” region at the center needs every pip to match — nothing else fits. Place the 1–5 domino vertically on row 2, column 3 and row 3, column 3.
5. Row 2, column 2 has only one open neighbor, so its domino must run to row 3, column 2; the “=” region at the center needs every pip to match (1 of its 2 cells is already filled) — nothing else fits. Place the 5–6 domino vertically on row 2, column 2 and row 3, column 2.

Start with the “<6” region at the center: the only way to make it with these dominoes is 1 + 1 + 1 + 2.

• the single-cell “<6” region at the top-left: 5
• the single-cell “<4” region at the top-right: 3
• the “<6” region at the center: 1, 1, 1, 2
• the “=” region at the right: 6, 6
• the “=” region at the right: 4, 4
• the single-cell “<5” region at the left: 3
• the single-cell “<3” region at the bottom: 2

1. The “<6” region at the center must total less than 6 — 7 placements fit here for now, but every other one leaves some region impossible a few moves later. Place the 1–3 domino horizontally on row 3, column 1 and row 3, column 2.
2. The single-cell “<3” region at the bottom must total less than 3 — 4 placements fit here for now, but every other one leaves some region impossible a few moves later. Place the 2–2 domino vertically on row 3, column 3 and row 4, column 3.
3. Row 1, column 2 has only one open neighbor, so its domino must run to row 2, column 2; the single-cell “<6” region at the top-left must total less than 6 — nothing else fits. Place the 1–5 domino vertically on row 1, column 2 and row 2, column 2.
4. Row 2, column 3 has only one open neighbor, so its domino must run to row 2, column 4; the “<6” region at the center must total less than 6 (3 of its 4 cells are already filled) — nothing else fits. Place the 1–6 domino horizontally on row 2, column 3 and row 2, column 4.
5. The “=” region at the right needs every pip to match — 2 placements fit here for now, but every other one leaves some region impossible a few moves later. Place the 3–4 domino vertically on row 1, column 5 and row 2, column 5.
6. The “=” region at the right needs every pip to match (1 of its 2 cells is already filled) — nothing else fits. Place the 3–6 domino vertically on row 3, column 4 and row 4, column 4.
7. Row 3, column 5 has only one open neighbor, so its domino must run to row 4, column 5; the “=” region at the right needs every pip to match (1 of its 2 cells is already filled) — nothing else fits. Place the 4–4 domino vertically on row 3, column 5 and row 4, column 5.

Start with the 4 region at the bottom-left: the only way to make it with these dominoes is 1 + 1 + 2.

• the “=” region at the top-left: 6, 6
• the 8 region at the top: 3, 5
• the “=” region at the top-left: 5, 5
• the “=” region at the top: 3, 3
• the 5 region at the top-right: 1, 2, 2
• the 12 region at the right: 6, 6
• the 4 region at the bottom-left: 1, 1, 2
• the “=” region at the left: 4, 4, 4
• the single-cell 4 region at the right: 4
• the single-cell 4 region at the right: 4
• the single-cell 4 region at the bottom: 4
• the 15 region at the bottom-right: 5, 5, 5
• the 5 region at the bottom-right: 2, 3
• the single-cell “<3” region at the bottom: 1

1. The single-cell 4 region at the bottom needs a total of exactly 4 — nothing else fits. Place the 1–4 domino vertically on row 5, column 4 and row 6, column 4.
2. The 4 region at the bottom-left needs a total of exactly 4 — 2 placements fit here for now; this one matches the official answer (this board has more than one valid layout). Place the 1–1 domino vertically on row 5, column 1 and row 6, column 1.
3. The single-cell 4 region at the right needs a total of exactly 4 — 2 placements fit here for now; this one matches the official answer (this board has more than one valid layout). Place the 4–6 domino horizontally on row 4, column 7 and row 4, column 8.
4. Row 5, column 8 has only one open neighbor, so its domino must run to row 6, column 8; the 5 region at the bottom-right needs a total of exactly 5 — 2 placements fit here for now; this one matches the official answer (this board has more than one valid layout). Place the 2–3 domino vertically on row 5, column 8 and row 6, column 8.
5. Row 2, column 6 has only one open neighbor, so its domino must run to row 2, column 7; the 5 region at the top-right needs a total of exactly 5 — nothing else fits. Place the 2–2 domino horizontally on row 2, column 6 and row 2, column 7.
6. Row 2, column 8 has only one open neighbor, so its domino must run to row 3, column 8; the 5 region at the top-right needs a total of exactly 5 (2 of its 3 cells are already filled) — nothing else fits. Place the 1–6 domino vertically on row 2, column 8 and row 3, column 8.
7. The 4 region at the bottom-left needs a total of exactly 4 (2 of its 3 cells are already filled) — 2 placements fit here for now; this one matches the official answer (this board has more than one valid layout). Place the 2–5 domino vertically on row 3, column 1 and row 4, column 1.
8. Row 4, column 2 has only one open neighbor, so its domino must run to row 4, column 3; the “=” region at the left needs every pip to match — 2 placements fit here for now; this one matches the official answer (this board has more than one valid layout). Place the 4–4 domino horizontally on row 4, column 2 and row 4, column 3.
9. Row 4, column 4 has only one open neighbor, so its domino must run to row 3, column 4; the “=” region at the left needs every pip to match (2 of its 3 cells are already filled) — 2 placements fit here for now; this one matches the official answer (this board has more than one valid layout). Place the 3–4 domino vertically on row 3, column 4 and row 4, column 4.
10. Row 4, column 6 has only one open neighbor, so its domino must run to row 5, column 6; the single-cell 4 region at the right needs a total of exactly 4 — nothing else fits. Place the 4–5 domino vertically on row 4, column 6 and row 5, column 6.
11. Row 6, column 6 has only one open neighbor, so its domino must run to row 6, column 7; the 15 region at the bottom-right needs a total of exactly 15 (1 of its 3 cells is already filled) — nothing else fits. Place the 5–5 domino horizontally on row 6, column 6 and row 6, column 7.
12. The “=” region at the top-left needs every pip to match — 2 placements fit here for now; this one matches the official answer (this board has more than one valid layout). Place the 5–6 domino vertically on row 1, column 1 and row 2, column 1.
13. Row 1, column 2 has only one open neighbor, so its domino must run to row 1, column 3; the “=” region at the top-left needs every pip to match (1 of its 2 cells is already filled) — nothing else fits. Place the 3–6 domino horizontally on row 1, column 2 and row 1, column 3.
14. Row 1, column 4 has only one open neighbor, so its domino must run to row 2, column 4; the 8 region at the top needs a total of exactly 8 (1 of its 2 cells is already filled) — nothing else fits. Place the 3–5 domino vertically on row 1, column 4 and row 2, column 4.

This board has more than one valid layout; the steps follow the official answer.